I have a 2D graphic which contains a table of curves within a circular region.

rotateparametric[parfunc_, fixedpoint_, angle_] := 
  RotationMatrix[angle].(parfunc - fixedpoint) + fixedpoint;
viewAngle = Pi/3;
ctrVolume = {(Exp[(Pi - viewAngle)*0.5] + 1)/2, 0};
radiusVolume = (Exp[(Pi - viewAngle)*0.5] - 1)/2;
radiusRing = (Exp[(Pi - viewAngle)*0.5] + 1)/2;
FPS = 120*3;
fPlanet = 3; 
fOrbit = 10;
radiusEquation = Exp[t*0.5];
planetRotation = 
 rotateparametric[{radiusEquation*Cos[t], radiusEquation*Sin[t]}, {0, 
   0}, -2*Pi*i*fPlanet/FPS]
mirrorPlanetRotation = 
 rotateparametric[{radiusEquation*Cos[t], radiusEquation*Sin[t]}, {0, 
   0}, Pi - 2*Pi*i*fPlanet/FPS]
orbitRotation = 
 rotateparametric[planetRotation, ctrVolume, +2*Pi*i*fOrbit/FPS]
mirrorOrbitRotation = 
 rotateparametric[planetRotation, ctrVolume, Pi + 2*Pi*i*fOrbit/FPS]
TheCurves = Evaluate@Table[orbitRotation, {i, 1, FPS}];
TheMirrorCurves = Evaluate@Table[mirrorOrbitRotation, {i, 1, FPS}];
pp = ParametricPlot[{TheCurves, TheMirrorCurves}, {t, 0, 
   Pi - viewAngle}, 
  RegionFunction -> (Norm[{#, #2} - ctrVolume] <= radiusVolume &), 
  PlotRange -> All]

This is the output:

What I want to do is first, divide the region into discrete little regions (meshes) which I will be the decider to the size of the mesh. For example, see below figure:

Then I need to extract the tangent values of each curve within the mesh so I can calculate its perpendicular vector's angle as below:

If it will be help, I need this to calculate the minimum voxel in a holographic volume. When I find the perpendicular vectors' angles I will know the total view angle of a voxel (mesh). If the total angle of each voxel covers 360 degree than it means I hit my goal. Thanks.